Assume we are living in a computer simulation

Any computer program can be modeled by a particular Turing machine. A Turing machine has a countably infinite state. That implies that the universe that we 'live' in has a countably infinite state. That means that in between two different points in space there is a finite number of position. In real number based models there would be an uncountably infinite number of positions. That also means that in between two different times instead of being an uncountably infinite number of times there is a finite number of times.

How many position would be between two different points. There is a number called the Planck length that "is believed to be the shortest meaningful length, the limiting distance below which the very notions of space and length cease to exist". That is consistent with the universal being countably infinite. There also is a notion of Planck time which is also consistent with reality being countably infinite. I wonder what things become true if you assume the universe is countably infinite that would not be true if you assume the universe is uncountably finite.

If the universe was a finite but perhaps increasing size then that implies the number of position and things in the universe is finite. For that case Godel's incompleteness theorem does not apply. Since the model for the universe would not be capable of representing whole numbers. That would also imply that any theorem could theoretically be proven through enumeration. That is not practical but still theoretically possible unlike the case when Godel's incompleteness theorem applies.